Starting from known determinantal representation of outer inverses we derive their determinantal representation in terms of the inner product in the Euclidean space. Subsequently, we define the double inner product of two miscellaneous tensors of rank 2 in a Riemannian space. Corresponding determinantal representation as well as the general representation of outer inverses in the Riemannian space is derived. A nonzero {2}-inverse X of a given tensor A obeying ρ(X) = s, 1 ≤ s ≤ r = ρ(A) is

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... sed in terms of the double inner product involving compound tensors with minors of the order s, extracted from A and appropriate tensors. AMS Subj. Class.: 15A09, 15A69, 53A45.